Question: Christopher is 3 times as old as Nadia. Eight years ago, Christopher was 5 times as old as Nadia. How old is Nadia now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Nadia. Let Christopher's current age be $c$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $c = 3n$ Eight years ago, Christopher was $c - 8$ years old, and Nadia was $n - 8$ years old. The information in the second sentence can be expressed in the following equation: $c - 8 = 5(n - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = 3n$ . Substituting this into our second equation, we get: $3n$ $-$ $8 = 5(n - 8)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $3 n - 8 = 5 n - 40$ Solving for $n$ , we get: $2 n = 32.$ $n = 16$.